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Applications of line objects in robotics. (English) Zbl 1046.70004
Summary: The Lie algebra of Lie group of Euclidean motions in $$E_3$$ is represented as the vector space $$A_6$$ of couples of vectors in $$E_3$$. We describe all subalgebras and all 3-dimensional subspaces of $$A_6$$ which are orthogonal to themselves according to the Klein form, and give their kinematic interpretations. Vector fields in $$E_3$$ determined by elements of $$A_6$$ and their kinematic and dynamic interpretations are investigated.

##### MSC:
 70B15 Kinematics of mechanisms and robots 70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics 22E70 Applications of Lie groups to the sciences; explicit representations
##### Keywords:
Lie algebra; Lie group; Euclidean motions; Klein form